This paper presents an analytical study of the tapered double-cantilever-beam (DCB) fracture mechanics test of polymeric adhesives and joints. The test specimen consists of high modulus metal adherends bonded together by a thin layer, low modulus adhesive. The fracture of the joint is modeled by the growth of a cohesive crack in the adhesive bond. The analysis employs an advanced hybrid-stress finite element method based on the formulation of Muskhelishvili's complex stress functions through a modified complementary energy principle. Numerically exact solutions are obtained for the joints with various geometries and material parameters. The crack-tip stress field, the associated stress intensity factor, and the energy release rate are determined quantitatively for each case. Characteristics of the specimen response and fundamental differences in the crack-tip behavior between a monolithic material and the joint are revealed. Effects of the adherend/adhesive modulus ratio, adhesive layer thickness, specimen geometry, and crack length on the tests are studied. Approximations involved in test results due to the specimen design by a simple beam theory are determined also.